One-loop Research Articles

Gravitational corrections to the Einstein-scalar-QCD model

This study employs the effective field theory approach to quantum gravity to investigate a non-Abelian gauge theory involving scalar particles coupled to gravity. The study demonstrates explicitly that the Slavnov-Taylor identities are maintained at one-loop order, which indicates that the universality of the color charge is preserved. Additionally, the graviton corrections to the two-loop gluon self-energy and its renormalization are computed.

N-particle irreducible actions for stochastic fluids

We construct one- and two-particle irreducible (1PI and 2PI) effective actions for the stochastic fluid dynamics of a conserved density undergoing diffusive motion. We compute the 1PI action in one-loop order and the 2PI action in two-loop approximation. We derive a set of Schwinger-Dyson equations and regularize the resulting equations using Pauli-Villars fields. We numerically solve the Schwinger-Dyson equations for a non-critical fluid. We find that higher-loop effects summed by the Schwinger-Dyson renormalize the non-linear coupling. We also find indications of a diffuson-cascade, the appearance of n-loop correction with smaller and smaller exponential suppression.

The Analytic Wavefunction

The wavefunction in quantum field theory is an invaluable tool for tackling a variety of problems, including probing the interior of Minkowski spacetime and modelling boundary observables in de Sitter spacetime. Here we study the analytic structure of wavefunction coefficients in Minkowski as a function of their kinematics. We introduce an off-shell wavefunction in terms of amputated time-ordered correlation functions and show that it is analytic in the complex energy plane except for possible singularities on the negative real axis. These singularities are determined to all loop orders by a simple energy-conservation condition. We confirm this picture by developing a Landau analysis of wavefunction loop integrals and corroborate our findings with several explicit calculations in scalar field theories. This analytic structure allows us to derive new UV/IR sum rules for the wavefunction that fix the coefficients in its low-energy expansion in terms of integrals of discontinuities in the corresponding UV-completion. In contrast to the analogous sum rules for scattering amplitudes, the wavefunction sum rules can also constrain total-derivative interactions. We explicitly verify these new relations at one-loop order in simple UV models of a light and a heavy scalar. Our results, which apply to both Lorentz invariant and boost-breaking theories, pave the way towards deriving wavefunction positivity bounds in flat and cosmological spacetimes.

Gradient-flowed order parameter for spontaneous gauge symmetry breaking

The gauge-invariant two-point function of the Higgs field at the same spacetime point can make a natural gauge-invariant order parameter for spontaneous gauge symmetry breaking. However, this composite operator is ultraviolet divergent and is not well defined. We propose using a gradient flow to cure the divergence from putting the fields at the same spacetime point. As a first step, we compute it for the Abelian Higgs model with a positive mass squared at the one-loop order in the continuum theory using the saddle-point method to estimate the finite part. The order parameter consistently goes to zero in the infrared limit of the infinite flow time.

One-loop corrections to the neutrino mass in the axion–neutrino coupling scheme

The coupling between neutral scalar axions and neutrinos is discussed as a possible mechanism responsible for a nonzero neutrino mass. We add to the conventional Peccei and Queen zeroth-order approach, that is the breaking of the U(1) symmetry at the axion level added to the fourth component of the neutrino current, one-loop corrections assuming the composite nature of flavor neutrinos. The calculations are performed for the three active neutrino flavors.

Loop-level double-copy for massive fermions in the fundamental

We find that unitarity cuts and the duality between color and kinematics are sufficient constraints to bootstrap D-dimensional QCD scattering amplitudes starting from three-particle tree-level. Specifically, we calculate tree level amplitudes through six-points, as well as the four-point one-loop correction for massive fermions in the fundamental representation of the gauge group — constructing a color-dual representation of the latter for the first time. To do so we clarify a prescription for functional kinematic ansatze involving fermionic matter. The advantages of color-dual calculation, familiar from particles in the adjoint, also apply here: only a small number of basis topologies must be constrained via physical information of the theory, and algebraic relations propagate this to a full solution. As all the QCD amplitudes we construct here are color-dual, they trivially generate D-dimensional amplitudes in gravitational theories via double-copy construction.

Discrete time heat kernel and UV modified propagators with dimensional deconstruction

We revisit the dimensionally deconstructed scalar quantum electrodynamics and consider the (Euclidean) propagator of the scalar field in the model. Although we have previously investigated the one-loop effect in this model by obtaining the usual heat kernel trace, we adopt discrete proper-time heat kernels in this paper and aim to construct the modified propagator, which has improved behaviors in the ultraviolet region, by changing the range of sum of the discrete heat kernels.

SMEFT effects on the gravitational wave spectrum from an electroweak phase transition

Future gravitational wave observations are potentially sensitive to new physics corrections to the Higgs potential once the first-order electroweak phase transition arises. We study the SMEFT dimension-six operator effects on the Higgs potential, where three types of effects are taken into account: (i) SMEFT tree level effect on $\varphi^6$ operator, (ii) SMEFT tree level effect on the wave function renormalization of the Higgs field, and (iii) SMEFT top-quark one-loop level effect. The sensitivity of future gravitational wave observations to these effects is numerically calculated by performing a Fisher matrix analysis. We find that the future gravitational wave observations can be sensitive to (ii) and (iii) once the first-order electroweak phase transition arises from (i). The dimension-eight $\varphi^8$ operator effects on the first-order electroweak phase transition are also discussed. The sensitivities of the future gravitational wave observations are also compared with those of future collider experiments.

Collider probe of heavy additional Higgs bosons solving the muon g−2 and dark matter problems

We study the Large Hadron Collider (LHC) search potential of a $\mathbb{Z}_4$-based two Higgs doublet model which can simultaneously explain the muon $g-2$ anomaly and the observed dark matter. The neutral scalars in the second Higgs doublet couple to $\mu$ and $\tau$ and largely contribute to the muon anomalous magnetic moment through the one-loop diagram involving $\tau$ and scalars. An additional singlet scalar which is charged under the discrete symmetry can be a dark matter candidate. An upper limit on the scalar mass originates from the unitarity constraint, and the $\mu\tau$ flavor-violating nature of the scalars predicts non-standard signatures at the LHC. However, the previously proposed $\mu^\pm\mu^\pm\tau^\mp\tau^\mp$ signal via the electroweak heavy neutral scalar pair production at the LHC loses sensitivity for increasing scalar mass. We revisit this model and investigate the LHC prospects for the single production of the $\mu\tau$ flavor-violating neutral scalar. It is shown that the single scalar process helps to extend the LHC reach to the 1$\,$TeV mass regime of the scenario. The search potential at the high energy LHC is also discussed.

How Infrared Singularities Affect Nambu–Goldstone Bosons at Finite Temperatures

Ordered phases realized through broken continuous symmetries embrace long-range order-parameter fluctuations as manifest in the power-law decays of both the transverse and longitudinal correlations, which are similar to those at the second-order transition point. We calculate the transverse one-loop correction to the dispersion relation of nonrelativistic Nambu-Goldstone (NG) bosons at finite temperatures, assuming that they have well-defined dispersion relations with some integer exponents. It is found that the transverse correlations make the lifetime of the NG bosons vanish right on the assumed dispersion curve below three dimensions at finite temperatures. Combined with the vanishing of the longitudinal "mass", the result indicates that the correlations generally bring both an intrinsic lifetime to the excitations and a qualitative change in the dispersion relation at long wavelengths below three dimensions at finite temperatures, unless it is protected by some conservation law. A more detailed calculation performed specifically on a single-component Bose-Einstein condensate reveals that the gapless Bogoliubov mode predicted by the perturbative treatment is modified substantially after incorporating the correlations to have (i) an intrinsic lifetime and (ii) a peak shift at long wavelengths from the linear dispersion relation. Thus, the NG bosons may be fluctuating intrinsically into and out of the ordered "vacuum" to maintain the order temporally.

Cosmological perturbation theory using generalized Einstein–de Sitter cosmologies

The separable analytical solution in standard perturbation theory for an Einstein--de Sitter (EdS) universe can be generalized to the wider class of such cosmologies (``generalized EdS,'' or gEdS) in which a fraction of the pressureless fluid does not cluster. We derive the corresponding kernels in both Eulerian perturbation theory (EPT) and Lagrangian perturbation theory, generalizing the canonical EdS expressions to a one-parameter family where the parameter can be taken to be the exponent $\ensuremath{\alpha}$ of the growing mode linear amplification $D(a)\ensuremath{\propto}{a}^{\ensuremath{\alpha}}$. For the power spectrum (PS) at one loop in EPT, the contribution additional to standard EdS is given, for each of the ``13'' and ``22'' terms, as a function of two infrared safe integrals. In the second part of the paper we show that the calculation of cosmology-dependent corrections in perturbation theory in standard [e.g., Lambda cold dark matter (LCDM)] models can be simplified, and their magnitude and parameter dependence better understood, by relating them to our analytic results for gEdS models. At second order the time dependent kernels are equivalent to the analytic kernels of the gEdS model with $\ensuremath{\alpha}$ replaced by a single redshift dependent effective growth rate ${\ensuremath{\alpha}}_{2}(z)$. At third order the time evolution can be conveniently parametrized in terms of two additional such effective growth rates. For the PS calculated at one-loop order, the correction to the PS relative to the EdS limit can be expressed in terms of just ${\ensuremath{\alpha}}_{2}(z)$, one additional effective growth rate function, and the four infrared safe integrals of the gEdS limit. This is much simplified compared to expressions in the literature that use six or eight redshift dependent functions and are not explicitly infrared safe. Using the analytic gEdS expression for the PS with $\ensuremath{\alpha}={\ensuremath{\alpha}}_{2}(z)$ gives a good approximation (to $\ensuremath{\sim}25%$) for the exact result.

Massive theta lifts

We use Poincaré series for massive Maass-Jacobi forms to define a “massive theta lift”, and apply it to the examples of the constant function and the modular invariant j-function, with the Siegel-Narain theta function as integration kernel. These theta integrals are deformations of known one-loop string threshold corrections. Our massive theta lifts fall off exponentially, so some Rankin-Selberg integrals are finite without Zagier renormalization.

One-loop electron mass and QED trace anomaly

Electron mass is considered as a matrix element of the energy–momentum trace in the rest frame. The one-loop diagrams for this matrix element are different from the textbook diagrams for the electron mass renormalization. We clarify connection between the two sets of diagrams and explain analytically and diagrammatically why the results of both calculations coincide.

One-loop Lipatov vertex in QCD with higher ϵ-accuracy

The effective Reggeon-Reggeon-gluon vertex, known as Lipatov vertex, is the key ingredient that allows to develop the BFKL approach in QCD. Within the next-to-leading logarithmic approximation, it is sufficient to know its one-loop corrections, in dimensional regularization (D = 4 + 2ϵ), up to the constant term in the ϵ-expansion. In the next-to-next-to-leading approximation, however, the one-loop Lipatov vertex is needed up to the order ϵ2. In this paper we present the expression for this vertex in dimensional regularization up to the required accuracy.

One-loop fermion-photon vertex in arbitrary gauge and dimensions: A novel approach

We compute a one-loop electron-photon vertex with fully off-shell external momenta in an arbitrary covariant gauge and space-time dimension. There exist numerous efforts in literature where a one-loop off-shell vertex is calculated by employing the standard first-order Feynman rules in different covariant gauges and space-time dimensions of interest. The tensor structure which decomposes this three-point vertex into the components transverse and longitudinal to the photon momentum gets intertwined in this first-order formalism. The Ward-Takahashi identity is explicitly invoked to untangle the two pieces and the results are expressed in a preferred basis of 12 spin amplitudes. We propose a novel approach based upon an efficient combination of the first- and second-order formalisms of quantum electrodynamics to compute this one-loop vertex. Among some conspicuous advantages is the fact that this less known second-order formalism separates the spin and scalar degrees of freedom of an electron interacting electromagnetically. More noticeably, the longitudinal and transverse contributions naturally disentangle from the onset in our approach. Moreover, this decomposition leads to identities between one-loop scalar Feynman integrals with higher powers in the propagators and shifted space-time dimensions that can be used to prove the Ward-Takahashi identity at one-loop order without the need to evaluate any Feynman integral. Additionally, this natural decomposition allows us to establish the gauge independence of the Pauli form factor through explicit cancellations of scalar Feynman integrals that depend on the gauge parameter. These cancellations naturally lead to a compact expression for the Pauli form factor in arbitrary dimensions. Wherever necessary and insightful, we make comparisons with earlier works.

One-loop corrections to the celestial chiral algebra from Koszul Duality

We consider self-dual Yang-Mills theory (SDYM) in four dimensions and its lift to holomorphic BF theory on twistor space. Following the work of Costello and Paquette, we couple SDYM to a quartic axion field, which guarantees associativity of the (extended) celestial chiral algebra at the quantum level. We demonstrate how to reproduce their one-loop quantum deformation to the chiral algebra using Koszul duality.

Thermal quantum gravity in a general background gauge

We calculate in a general background gauge, to one-loop order, the leading logarithmic contribution from the graviton self-energy at finite temperature $T$, extending a previous analysis done at $T=0$. The result, which has a transverse structure, is applied to evaluate the leading quantum correction of the gravitational vacuum polarization to the Newtonian potential. An analytic expression valid at all temperatures is obtained, which generalizes the result obtained earlier at $T=0$. One finds that the magnitude of this quantum correction decreases as the temperature rises.

Wide-angle and relativistic effects in Fourier-space clustering statistics

Galaxy power spectrum and bispectrum signals are distorted by peculiar velocities and other relativistic effects arising from a perturbed spacetime background. In addition, study of correlation functions of tracers in Fourier space is often done in the plane-parallel approximation under which it is assumed that line-of-sight (LOS) vectors are parallel. In this work we show that a simple perturbative procedure can be employed for a fast evaluation of beyond plane-parallel (wide-angle) corrections to the power spectrum and bispectrum. We also show that evolution of linear matter density fluctuations in a relativistic context can be found from a simple method. For the power spectrum at linear level, we compare leading order wide-angle contributions to multipoles of the galaxy power spectrum with those from non-integrated and integrated relativistic corrections and estimate their possible contamination on local fNL measurements to be of order a few. We also compute wide-angle corrections in the presence of nonlinear terms at one-loop order. For the bispectrum, we show that wide-angle effects alone, even with fully symmetric choices of LOS, give rise to imaginary, odd-parity multipoles of the galaxy bispectrum (dipole, octupole, etc.) which are in many cases larger than previously known ones of relativistic origin. We calculate these contributions and provide an estimator for measuring the leading order bispectrum dipole from data, using a symmetric LOS definition. Finally, we calculate the leading order corrections to multipoles of real plane-parallel bispectrum multipoles and estimate the apparent local fNL induced to be of order unity.

QCD equation of state at finite isospin density from the linear sigma model with quarks: The cold case

We use the two-flavor Linear Sigma Model with quarks to study the phase structure of isospin asymmetric matter at zero temperature. The meson degrees of freedom provide the mean field chiral and isospin condensates on top of which we compute the effective potential accounting for constituent quark fluctuations at one-loop order. Using the renormalizability of the model, we absorb the ultraviolet divergences into suitable counterterms that are added respecting the original structure of the theory. These counterterms are determined from the stability conditions which require the effective potential to have minima in the condensates directions at the classical values, as well as the transition from the noncondensed to the condensed phase to be smooth as a function of the isospin chemical potential. We use the model to study the evolution of the condensates as well as the pressure, energy and isospin densities and the sound velocity as functions of the isospin chemical potential. The approach does a good average description up to isospin chemical potentials values not too large as compared to the vacuum pion mass.

Missing one-loop contributions in secondary gravitational waves

We find several missing one-loop-order contributions in previous considerations about secondary gravitational waves induced at nonlinear order in cosmological perturbations. We consider a consistent perturbative expansion to third order in cosmological perturbations, including higher-order interactions and iterative solutions ignored in the previous literature. Tensor fluctuations induced by the source with two scalar and one tensor perturbations are correlated with the first-order tensor fluctuation and thus give a one-loop order correction to the tensor-power spectrum. The missing loop correction is scale invariant and negative in the superhorizon region, which secondarily reduces the initial primordial tensor-power spectrum prior to the horizon reentry. Such an IR behavior is very different from the autospectrum of second-order induced tensor modes discussed in the previous literature and can be important for the actual gravitational wave measurements. For a sharp peak of scalar fluctuations with ${A}_{\ensuremath{\zeta}}={10}^{\ensuremath{-}2}$ at ${k}_{*}={10}^{5}\text{ }h/\mathrm{Mpc}$ motivated by the LIGO/Virgo events, we show that the tensor-power spectrum at the cosmic microwave background scale reduces by at most 35%. Hence, the polarization B mode might not be seen because of the reduction of the original tensor spectrum due to the secondary effect of primordial black hole formation.